Subset selection in multiple linear regression in the presence of outlier and multicollinearity

Various subset selection methods are based on the least squares parameter estimation method. The performance of these methods is not reasonably well in the presence of outlier or multicollinearity or both. Few subset selection methods based on the M-estimator are available in the literature for outl...

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Bibliographic Details
Published in:Statistical methodology 2014-07, Vol.19, p.44-59
Main Authors: Jadhav, Nileshkumar H., Kashid, Dattatraya N., Kulkarni, Subhash R.
Format: Article
Language:English
Subjects:
Jackknifed ridge [formula omitted]-estimator
Multicollinearity
Multiple linear regression
Outlier
Subset selection
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Summary:Various subset selection methods are based on the least squares parameter estimation method. The performance of these methods is not reasonably well in the presence of outlier or multicollinearity or both. Few subset selection methods based on the M-estimator are available in the literature for outlier data. Very few subset selection methods account the problem of multicollinearity with ridge regression estimator. In this article, we develop a generalized version of Sp statistic based on the jackknifed ridge M-estimator for subset selection in the presence of outlier and multicollinearity. We establish the equivalence of this statistic with the existing Cp, Sp and Rp statistics. The performance of the proposed method is illustrated through some numerical examples and the correct model selection ability is evaluated using simulation study.
ISSN:1572-3127
1878-0954
DOI:10.1016/j.stamet.2014.02.002